Phonon-Mode Calculation, Far- and Mid-Infrared, and Raman Spectra

Article pubs.acs.org/JPCC

Phonon-Mode Calculation, Far- and Mid-Infrared, and Raman Spectra of an ε‑Ga0.5Fe1.5O3 Magnet Shin-ichi Ohkoshi,*,† Marie Yoshikiyo,† Yoshikazu Umeta,† Masaya Komine,† Rei Fujiwara,‡ Hiroko Tokoro,†,‡ Kouji Chiba,§ Takeo Soejima,∥ Asuka Namai,† Yasuto Miyamoto,† and Tomomichi Nasu† †

Department of Chemistry, School of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan Division of Materials Science, Faculty of Pure and Applied Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan § Science and Technology System Div., Ryoka Systems Inc., Tokyo Skytree East Tower, 1-1-2 Oshiage, Sumida-ku, Tokyo 131-0045, Japan ∥ JASCO Corporation, 2967-5 Ishikawa-machi, Hachioji, Tokyo 192-8537, Japan ‡

S Supporting Information *

ABSTRACT: Gallium-substituted epsilon iron oxide (εGa0.5Fe1.5O3) has drawn attention because its millimeter wave absorption frequency meets the millimeter wave radar frequency for automobiles. We report the phonon modes of εGa0.5Fe1.5O3, which has an orthorhombic structure in the Pna21 space group. First-principles phonon-mode calculations show that ε-Ga0.5Fe1.5O3 has 117 optical phonon modes (fundamental vibrations) with symmetries of A1, A2, B1, and B2 as well as three acoustic phonon modes. The phonon density of states demonstrates that the movements of Fe and Ga contribute to the phonon modes in the lower energy region of 20−370 cm−1, while the movements of O contribute to the phonon modes in the higher energy region of 370−720 cm−1. We directly measure the optical phonon modes of ε-Ga0.48Fe1.52O3 nanoparticles using far- and mid-infrared (IR) and Raman spectroscopies, which agree well with those obtained by first-principles phonon-mode calculations. Additionally, the thermodynamic parameters of the internal energy (U), the vibrational entropy (Svib), and the Helmholtz energy (A) are calculated and understood through the investigation of the phonon modes. Heat capacity measurements confirm that the observed thermodynamic parameters are consistent with the predicted values. ties, and millimeter-wave absorption properties in the εphase.16−18,32,33 For example, in the case of rhodiumsubstituted ε-Fe2O3, the coercive field is enhanced to 31 kOe at room temperature, while indium-substituted ε-Fe2O3 exhibits a ferri-antiferromagnetic phase transition at a temperature that is about half of the Curie temperature. Gallium-substituted εFe2O3 (ε-Ga0.5Fe1.5O3) has drawn attention because its millimeter-wave absorption frequency meets the millimeterwave radar frequency of 76 GHz for automobiles. In this study, first-principles phonon-mode calculations are performed for εGa0.5Fe1.5O3, in which the tetrahedral Fe3+ (S = 5/2) sites are replaced by nonmagnetic Ga3+ (S = 0). We report the phonon density of states, optical transition moments, and atomic movements of the phonon modes in ε-Ga0.5Fe1.5O3 via firstprinciples calculations. Additionally, the optical phonon modes of ε-Ga0.48Fe1.52O3 nanoparticle are directly measured using far-

1. INTRODUCTION Iron ferrites have been used as magnetic materials in various devices (e.g., magnetic motors, magnetic recording media, magnetic fluids, and electromagnetic wave filters).1−13 Epsilon iron oxide (ε-Fe2O3), which is a polymorph of ferric oxide (Fe2O3), has drawn much attention due to its large coercive field of 25 kOe,14,15 high-frequency millimeter wave absorption,16−18 and so on.19−28 ε-Fe2O3 can be downsized to the sub-10 nanometer level because of its strong magnetic anisotropy, realizing the smallest hard magnetic ferrite.29 Theoretical calculations of ε-Fe2O3 have been performed to understand its physical properties.29−31 For example, periodic structure calculations clarify that ε-Fe2O3 is a charge-transfertype insulator with a very wide bandgap.29,30 Moreover, the strong magnetic anisotropy of this material is attributed to the strong hybridization between Fe 3d and O 2p orbitals. Recently, calculations have been undertaken to determine its theoretical phonon modes.15 The Fe3+ ion of ε-Fe2O3 can be replaced by other metal cations. Such a metal replacement is useful for controlling the magnetic properties, optical proper© XXXX American Chemical Society

Received: December 17, 2016 Revised: February 23, 2017 Published: February 27, 2017 A

DOI: 10.1021/acs.jpcc.6b12694 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

and C sites and Ga3+ ion at the tetrahedral D site; hereafter these are defined as Fe(A), Fe(B), Fe(C), and Ga(D), respectively. There are also six different O sites [O(1)− O(6)]. Figure 1 and Figure S1 show the unit cell of εGa0.5Fe1.5O3, and Table S1 shows the optimized atomic positions.

and mid-infrared (IR) and Raman spectroscopies. On the basis of the phonon-mode calculations, the thermodynamic parameters are estimated and compared with the heat capacity measurements.

2. EXPERIMENTAL SECTION 2.1. First-Principles Phonon-Mode Calculation. Phonon-mode calculations of ε-Ga0.5Fe1.5O3 were carried out using the Phonon code34 in the Material Design MedeA package. To calculate the phonon modes, the direct method implemented in the Phonon code was used with 2 pm displacements using the optimized structures with a 2 × 1 × 1 supercell. The atomic positions were optimized using the Vienna ab initio Simulation Package (VASP)35,36 with an energy cutoff of 520 eV and 5 × 3 × 3 k-mesh until the 10−5 eV pm−1 force tolerance was satisfied. Splitting of the longitudinal phonon modes and transversal phonon modes was taken into account to calculate the transition moment for the IR activity. The electronic energy of formation referenced to elements in the standard state was calculated using the standard generalized gradient approximation (GGA). 2.2. Synthesis. Gallium-substituted ε-Fe2O3, which is close to ε-Ga0.5Fe1.5O3, was synthesized using the sol−gel technique according to the literature.16 A mixed aqueous solution of Fe(NO3)3 (0.26 mol dm−3) and Ga(NO3)3 (0.08 mol dm−3) was prepared and a NH3 aqueous solution (1.3 mol dm−3) was added while rapidly stirring. Next, tetraethoxysilane was added dropwise to the solution to form a silica matrix around the Fe, Ga hydroxide. The mixture was stirred for 20 h, and the precipitates were washed, dried, and sintered in air at 1100 °C for 4 h. Then, the silica matrix was removed by chemical etching using a NaOH solution. 2.3. Physical Measurements. Elemental analyses of the obtained sample were performed using inductively coupled plasma-atomic emission spectroscopy (ICP-AES, Jarrel-Ash, IRIS/AP). Transmission electron microscopy (TEM) measurements were carried out using a JEOL 100CXII, and X-ray diffraction (XRD) measurements were conducted on a Rigaku Ultima IV with Cu Kα radiation (λ = 1.5406 Å) at room temperature. The magnetic properties were measured with a superconducting quantum interference device (SQUID) magnetometer (Quantum Design, MPMS 7), while the electromagnetic wave absorption property was measured in the range of 1.7−50 cm−1 using a terahertz time-domain spectroscopy (THz-TDS) system (Advantest, TAS7x00TS). Far-IR spectra in the range of 60−600 cm−1 were recorded using a JASCO FT-IR 6100 spectrometer with samples rubbed on polyethylene plates in a vacuum chamber at room temperature. Mid-IR spectra in the range above 600 cm−1 were measured using a SHIMADZU FTIR-8200PC with a pellet of ε-Ga0.48Fe1.52O3 powder dispersed in KBr. Raman spectra were measured using a Raman microspectrometer (JASCO NRS-5100). The heat capacity was measured using a physical property measurement system (PPMS).

Figure 1. Crystal structure. Crystal structure of ε-Ga0.5Fe1.5O3 shown as polyhedra. Red, orange, and light-blue balls represent Fe at A, B, and C sites, Ga at D sites, and O sites, respectively.

The phonon-mode calculations of ε-Ga0.5Fe1.5O3 reveal 117 optical phonon modes (fundamental vibrations) and 3 acoustic phonon modes. Table 1 shows the resonance energies, symmetries, and IR and Raman activities of the optical phonon modes. The A1, A2, B1, and B2 symmetries are Raman-active, while the A1, B1, and B2 symmetries are also IR-active. Figure 2a shows the phonon dispersion of ε-Ga0.5Fe1.5O3. The solid and dotted lines indicate the optical phonon modes and the acoustic phonon modes, respectively. Figure S2 shows the energy diagram of the optical phonon modes at the Γ point. The right side shows the optical phonon modes for each symmetry. Figure 2b shows the phonon density of states of εGa0.5Fe1.5O3 and the partial phonon density of states for Fe(A)−Fe(C), Ga(D), and O(1)−O(6) sites. Fe and Ga of the heavy metal elements mainly contribute to the phonon modes in the low-energy region of 20−370 cm−1, whereas O of the light element mainly contributes to the phonon modes in the energy range of 370−720 cm−1. Interestingly, the density of states in the high-energy range of 570−720 cm−1 is affected by Ga(D) and O(3), where O(3) is connected to Ga(D). The optical transition moments for the IR activities were calculated. In the IR-active phonon modes, the lowest and highest energy transitions are at 87.79 (A1) and 725.9 cm−1 (B1), respectively (Table 1). There are 117 optical phonon modes between these energies. The optical transitions of the following energies have strong absorbances: 87.79 (A1), 110.5 (B2), 126.7 (A1), 142.2 (B2), 154.5 (B2), 170.9 (B2), 187.5 (B2), 203.1 (B1), 226.4 (B2), 252.9 (B2), 269.3 (B2), 292.3 (B2), 316.0 (B1), 349.4 (B2), 387.1 (B2), 428.3 (B1), 488.7 (B2), 504.2 (B2), 580.7 (B2), 616.7 (B1), 705.9 (B2), and 725.9 cm−1 (B1). Figure 3 shows the calculated IR spectrum. In the phonon mode at 87.79 cm−1 (A1) of the lowest vibration mode, the layers parallel to the ab-plane containing the Fe and Ga atoms shift in the a-axis direction, as indicated in Figures 3 (left) and 4a (see Supporting Movie S1). In the phonon mode of 226.4 cm−1 (B2), the two Ga(D)−O(3) bonds at the tetrahedral Ga(D)O4 site twist and are accompanied by the bending mode of O(3)−Fe(B)−O(6) (Figure 4b, Movie S2). In the phonon mode of 387.1 cm−1 (B2), the Ga(D)−O(1) and Ga(D)−O(5) bonds at the tetrahedral Ga(D)O4 site twist, stretch, and are accompanied by the bending mode of O(1)−Fe(C)−O(4)

3. RESULTS AND DISCUSSION 3.1. First-Principles Calculations of the Phonon Modes. The phonon modes of ε-Ga0.5Fe1.5O3 were calculated using the Phonon code. Ga-substituted ε-Fe2O3 has an orthorhombic structure in the Pna21 space group with four nonequivalent metal cation sites (A−D sites).16 The crystal structure of ε-Ga0.5Fe1.5O3 has Fe3+ ions at the octahedral A, B, B


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The Journal of Physical Chemistry C Table 1. Optical Phonon Modes of ε-Ga0.5Fe1.5O3 Obtained by First-Principles Calculationsa

a

cm−1

sym.

R

IR

cm−1

sym.

R

IR

cm−1

sym.

R

IR

87.79 97.77 110.5 118.8 121.6 121.9 123.5 126.7 132.8 142.2 143.9 145.4 154.0 154.5 159.3 165.2 170.9 172.3 173.9 174.6 187.5 197.5 202.6 203.1 203.4 207.7 217.3 223.2 224.2 226.4 233.0 235.3 235.5 239.3 243.6 252.9 253.9 260.5 263.0

A1 A2 B2 A2 A1 B1 B1 A1 A2 B2 A1 B1 A1 B2 A2 A2 B2 A1 A2 B1 B2 A1 B1 B1 A2 B2 A2 B1 A1 B2 A2 B2 B1 A1 A2 B2 B1 B1 A2

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

O

265.3 269.3 270.8 280.6 283.1 286.5 292.3 293.7 300.2 301.7 305.1 309.3 316.0 318.9 320.1 328.6 336.4 339.9 342.8 349.4 352.6 353.5 362.3 363.4 377.4 378.7 380.4 386.8 387.1 387.1 391.9 403.1 408.0 409.8 419.4 423.4 428.3 430.7 432.4

A1 B2 B1 B1 A2 A1 B2 B1 B2 A2 A1 A2 B1 A2 A1 B2 B2 A1 B1 B2 B1 A1 A1 A2 B2 A1 B1 A2 B1 B2 A1 B2 A2 B1 A2 A1 B1 A2 A1


O O O O

432.4 450.2 452.6 464.3 471.5 488.7 488.8 494.4 504.2 509.9 512.9 514.5 534.4 545.9 564.6 580.7 585.7 590.8 592.5 604.2 612.8 616.7 624.2 625.3 637.2 641.1 642.4 647.7 649.4 654.4 663.3 670.2 672.3 675.6 680.8 695.8 705.6 705.9 725.9

B2 A1 B2 A2 A1 B2 B1 A2 B2 A2 B1 A1 B1 A2 B2 B2 A1 A2 A2 A1 B1 B1 B2 A1 B2 A1 B1 B2 A2 B1 A2 B2 A2 A1 B1 A1 A2 B2 B1


O O O

O O O O O O O O O O

O O O O O O O O O O O O O O O O O

O O O O O O O O O O O O O O O O O O O O O O O O O O

O O O O O O O O O O

O O O O O O O O O O O O O O O O

Wavenumber, symmetry, and activities of Raman/IR are listed.

contrary, the calculated formation energy of the electronic structure (U0) is −659.9 kJ mol−1. The sum of these energies indicates the internal energy (U) of the system; the U value at 0 K is −627.1 kJ mol−1 and increases with increasing temperature due to the phonon excitation. The heat capacity at a constant volume due to the lattice vibrations (Cv,vib) was also calculated. The vibrational entropy (Svib) increases with increasing temperature. Additionally, the electronic energy of formation was considered for the Helmholtz energy (A). The A value decreases with increasing temperature due to the contribution of Svib; the A value is −638.8 kJ mol−1 at 300 K. 3.2. Crystal Structure, Morphology, Magnetic Hysteresis Loop, and k = 0 Magnon Transition of εGa0.48Fe1.52O3. Gallium-substituted ε-Fe2O3, which is close to ε-Ga0.5Fe1.5O3, was synthesized according to the literature using the sol−gel technique.16 The formula of the obtained material is ε-Ga0.48Fe1.52O3. The TEM image shows spherical particles with an average size of 32.1 ± 14.9 nm (Figure 6a). Rietveld analysis of the XRD pattern indicates that the Ga ions

(Figure 4c, Movie S3). In these low-energy phonon modes, the Fe and Ga atoms mainly contribute to the lattice vibrations, while the movements of O contribute mostly in the higher energy region. For example, Figure 4d shows the phonon mode at 428.3 cm−1 (B1), which is a bending mode of O(1)−Ga(D)− O(5) at the tetrahedral Ga(D)O4 site (Movie S4). In the phonon mode at 695.9 cm−1 (A1), the Ga(D)−O(1), Ga(D)− O(3), and Ga(D)−O(5) bonds stretch simultaneously, changing the size of the Ga(D)O4 tetrahedron like a breathing mode. The neighboring tetrahedra expand and shrink in phase with each other (Figure 4e, Movie S5). The phonon mode at 725.9 cm−1 (B1) is the stretching mode of Fe(A)−O(4), Fe(A)−O(6), and Ga(D)−O(5), which causes the Ocontaining plane parallel to the ab-plane to elevate in the caxis direction (Figures 3 (right) and 4f, Movie S6). Furthermore, the thermodynamic parameters of εGa0.5Fe1.5O3 were also calculated (Figure 5). The vibrational internal energy (Uvib) is obtained from the phonon-mode calculations with a zero-point energy of 32.8 kJ mol−1. On the C


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Figure 2. Phonon dispersion and phonon density of states. (a) Phonon dispersion of ε-Ga0.5Fe1.5O3. Both the optical phonon dispersion (black lines) and acoustic phonon dispersion (dotted lines) are shown. (b) Calculated phonon density of states of ε-Ga0.5Fe1.5O3. Red, yellow, blue, and black lines indicate the contributions of Fe, Ga, O, and the total phonon density of states, respectively. Partial phonon density of states of Fe(A)− Fe(C), Ga(D), and O(1)−O(6) sites are shown.

Figure 3. Calculated IR spectrum and atomic movements of the phonon modes. (Center) Calculated IR spectrum of ε-Ga0.5Fe1.5O3. Black sticks denote the position of the IR-active modes, and red bars indicate the IR intensities of the phonon mode. (Left, right) Atomic movements of the representative phonon modes of ε-Ga0.5Fe1.5O3 at 87.79 (left) and 725.9 cm−1 (right). Red, yellow, and white balls represent Fe, Ga, and O atoms, respectively.

movements of the phonon modes calculated at 226.4 and 387.1 cm−1, respectively (Figure 4b,c). In the range of 400−600 cm−1, large broad peaks are observed around 440 and 500 cm−1. The peak at 440 cm−1 is assigned to the atomic movement of the phonon mode calculated at 428.3 cm−1 (Figure 4d). In the range of 600−750 cm−1, the IR peaks are observed at 635, 663, 698, and 727 cm−1. The IR peaks at 698 and 727 cm−1 are assigned to the atomic movements of the phonon modes calculated at 695.9 and 725.9 cm−1, respectively (Figure 4e,f). These high-energy phonon modes are attributed to the movements of Ga(D) and its surrounding O. The Raman spectrum of ε-Ga0.48Fe1.52O3 was measured as the reflections from the sample using a micro-Raman spectrometer (Figure 7b). In the Raman spectrum, 17 strong peaks (93, 123, 151, 158, 176, 205, 239, 258, 302, 360, 389, 454, 507, 567, 655, 687, and 741 cm−1) are observed. The peaks at 93, 176, 360, 687, and 741 cm−1 are much stronger than the IR spectrum of ε-Ga0.48Fe1.52O3. The Raman peaks of 93, 176, and 360 cm−1 correspond to the calculated Ramanactive modes at 97.77 (A2) (Figure 4g, Movie S7), 173.9 (A2),

mainly occupy the tetrahedral D site among the four nonequivalent cation sites (Table S2). The magnetic hysteresis loop of ε-Ga0.48Fe1.52O3 displays a saturation magnetization of 25.6 emu g−1 at 5 T and a coercive field of 6.7 kOe at 300 K (Figure 6b). The THz-TDS measurement confirms that εGa0.48Fe1.52O3 exhibits a millimeter wave absorption with a resonance frequency of 73 GHz (Figure 6b, inset). 3.3. Optical Phonon Modes Measured by Far- and Mid-IR and Raman Spectroscopies of ε-Ga0.48Fe1.52O3. Far- and mid-IR and Raman spectroscopic measurements were performed using a powder sample of ε-Ga0.48Fe1.52O3 nanoparticles (Figure 7 and Figure S3). Figure 7a shows the observed IR spectra accompanied by the calculated absorbance spectrum. In the energy range below 200 cm−1, eight peaks (92, 113, 127, 131, 151, 159, 175, and 188 cm−1), which correspond well to the phonon-mode calculations, are observed. The IR peak at 92 cm−1 is the atomic movement of the phonon mode calculated at 87.79 cm−1 (Figure 4a). In the range of 200−400 cm−1, IR peaks are observed at 222, 264, 296, 324, 352, and 389 cm−1. The peaks at 222 and 389 cm−1 originate from the atomic D


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Figure 4. Atomic movements of the phonon modes. Atomic movements of the representative phonon modes of ε-Ga0.5Fe1.5O3. Phonon modes at (a) 87.79, (b) 226.4, (c) 387.1, (d) 428.3, (e) 695.8, (f) 725.9, (g) 97.77, and (h) 705.6 cm−1. Red, orange, and blue balls represent Fe, Ga, and O atoms, respectively. Blue arrows indicate the movements of the atoms.

Figure 6. Physical properties of ε-Ga0.48Fe1.52O3 nanoparticles. (a) XRD pattern of ε-Ga0.48Fe1.52O3. Red crosses, black line, and gray line are the observed pattern, the calculated pattern, and their difference, respectively. Black tick marks represent the calculated positions of the Bragg reflections of ε-Ga0.48Fe1.52O3. Inset is the TEM image. (b) Magnetic hysteresis loop of ε-Ga0.48Fe1.52O3 measured at 300 K. Inset is millimeter wave absorption spectrum of ε-Ga0.48Fe1.52O3 measured at room temperature.

and 363.4 cm−1 (A2), respectively. The high energy peaks at 687 and 741 cm−1 are stronger than the IR spectrum from the Raman active phonon modes calculated at 672.3 (A2) and 705.6 cm−1 (A2) (Figure 4h, Movie S8), respectively. 3.4. Heat Capacity Measurements. To investigate the thermodynamic parameters, we measured the heat capacity (Cp) of ε-Ga0.48Fe1.52O3 (Figure 8b). The observed Cp plots

Figure 5. Thermodynamic parameters of ε-Ga0.5Fe1.5O3 obtained from first-principles phonon-mode calculations. Temperature dependence of (a) the internal energy (U), (b) the heat capacity (Cv,vib), (c) the vibrational entropy (Svib), and (d) the Helmholtz energy (A). E


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were fitted with the equation based on the two-Debye model37 (see Supporting Information, Section 6 for details). From the obtained Cp data, the enthalpy (H), the entropy (S), and the Gibbs energy (G) were also derived (Figure 8a,c,d). The obtained curves of H, Cp, S, and G are almost the same as the calculated thermodynamic parameters of U, Cv,vib, Svib, and A from the first-principles phonon-mode calculations under the approximation that the Gibbs energy corresponds to the Helmholtz energy for a solid material.

4. CONCLUSIONS ε-Ga0.5Fe1.5O3 is a distinct and useful analog of ε-Fe2O3 in terms of industrial applications, especially as a millimeter wave absorber for millimeter wave car radars. The first-principles phonon-mode calculations of ε-Ga0.5Fe1.5O3 show 117 optical phonon modes (fundamental vibrations) with symmetries of A1, A2, B1, and B2. The movements of Fe and Ga contribute to the phonon modes in the lower energy region, while the movements of O contribute to the phonon modes in the higher energy region. Far- and mid-IR and Raman spectroscopic measurements confirm that the observed spectra agree well with the calculated spectra. Additionally, the thermodynamic properties are understood through the investigation of the phonon modes.

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Figure 7. Far- and mid-IR spectra and Raman spectra. (a) Observed far- and mid-IR spectra of ε-Ga0.48Fe1.52O3 (red lines) and the calculated IR spectrum (black line). Black tick marks denote the positions of IR active modes, and red bars indicate the IR intensities. 60−600 cm−1 was measured by a far-IR spectrometer, and above 600 cm−1 was measured by a mid-IR spectrometer. (b) Observed Raman spectrum of ε-Ga0.48Fe1.52O3 (blue line). Black tick marks denote the calculated positions of the Raman-active modes.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b12694. Captions for Supplementary Movies, optimized atomic positions, crystal structure, energy diagram of each symmetry at Γ point, crystal structure parameters determined by Rietveld analysis, and thermodynamic analysis of heat capacity. (PDF) Supplementary Movie S1: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 87.79 cm−1 (A1). (MPG) Supplementary Movie S2: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 226.4 cm−1 (B2). (MPG) Supplementary Movie S3: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 387.1 cm−1 (B2). (MPG) Supplementary Movie S4: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 428.3 cm−1 (B1). (MPG) Supplementary Movie S5: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 695.8 cm−1 (A1). (MPG) Supplementary Movie S6: Atomic movement of the IR and Raman active phonon mode of ε-Fe2O3 at 725.9 cm−1 (B1). (MPG) Supplementary Movie S7: Atomic movement of the Raman active phonon mode of ε-Fe2O3 at 97.77 cm−1 (A2). (MPG) Supplementary Movie S8: Atomic movement of the Raman active phonon mode of ε-Fe2O3 at 705.6 cm−1 (A2). (MPG)

Figure 8. Thermodynamic parameters of ε-Ga0.48Fe1.52O3 obtained from heat capacity measurements. Temperature dependences of (a) the enthalpy (H), (b) the heat capacity (Cp), (c) the entropy (S), and (d) the Gibbs energy (G). Black dots and dotted line of Cp represent the observed data and the fitted curve based on the two-Debye model, respectively. H, S, and G are transformed from Cp.

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The Journal of Physical Chemistry C ORCID

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Shin-ichi Ohkoshi: 0000-0001-9359-5928 Author Contributions

All authors have given approval to the final version of the manuscript. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The present research was supported in part by a JSPS Grant-inAid for specially promoted Research (Grant Number 15H05697), a JSPS Grant-in-Aid for Young Scientists (A) and (B), and DOWA Technofund. M.K. gratefully acknowledges the support of the Advanced Leading Graduate Course for Photon Science (ALPS). Y.M. and T.N. are supported by Japan Society for the Promotion of Science through Program for Leading Graduate Schools (MERIT). We also recognize the Cryogenic Research Center, the University of Tokyo, and Nanotechnology Platform, which are supported by MEXT. We are grateful to Dr. K. Imoto for support with the THz-TDS measurements and Mr. T. Miyazaki, Mr. K. Masada, and Mr. T. Yoshida of DOWA Electronics Materials for the valuable discussions.

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